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© 1999

Random Walks in the Quarter-Plane

Algebraic Methods, Boundary Value Problems and Applications

Book

Table of contents

  1. Front Matter
    Pages I-XV
  2. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 1-6
  3. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 7-33
  4. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 35-49
  5. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 51-91
  6. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 93-127
  7. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 129-143
  8. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages 145-150
  9. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
    Pages E1-E4
  10. Back Matter
    Pages 151-154

About this book

Introduction

Historical Comments Two-dimensional random walks in domains with non-smooth boundaries inter­ est several groups of the mathematical community. In fact these objects are encountered in pure probabilistic problems, as well as in applications involv­ ing queueing theory. This monograph aims at promoting original mathematical methods to determine the invariant measure of such processes. Moreover, as it will emerge later, these methods can also be employed to characterize the transient behavior. It is worth to place our work in its historical context. This book has three sources. l. Boundary value problems for functions of one complex variable; 2. Singular integral equations, Wiener-Hopf equations, Toeplitz operators; 3. Random walks on a half-line and related queueing problems. The first two topics were for a long time in the center of interest of many well known mathematicians: Riemann, Sokhotski, Hilbert, Plemelj, Carleman, Wiener, Hopf. This one-dimensional theory took its final form in the works of Krein, Muskhelishvili, Gakhov, Gokhberg, etc. The third point, and the related probabilistic problems, have been thoroughly investigated by Spitzer, Feller, Baxter, Borovkov, Cohen, etc.

Keywords

Markov chain Riemann surfaces functional equations measure queuing theory random walk random walks uniformization

Authors and affiliations

  1. 1.Domaine de Voluceau, RocquencourtINRIALe ChesnayFrance
  2. 2.Department of MathematicsUniversity of OrléansOrléans la SourceFrance

Bibliographic information

  • Book Title Random Walks in the Quarter-Plane
  • Book Subtitle Algebraic Methods, Boundary Value Problems and Applications
  • Authors Guy Fayolle
    Roudolf Iasnogorodski
    Vadim Malyshev
  • Series Title Applications of Mathematics Stochastic Modelling and Applied Probability
  • DOI https://doi.org/10.1007/978-3-642-60001-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-65047-8
  • Softcover ISBN 978-3-642-64217-3
  • eBook ISBN 978-3-642-60001-2
  • Series ISSN 0172-4568
  • Edition Number 1
  • Number of Pages XV, 156
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
    Analysis
    Statistical Theory and Methods
  • Buy this book on publisher's site
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